Description:Many vital structures in complex biological systems are formed through the self-organization of initially disordered, discrete elements into coherent bodies. During cell division, for example, microtubules undergo microscopic interactions with molecular motors to form macroscopic structures including the cytoskeleton of daughter cells and the mitotic spindle which properly segregates chromosomes. Understanding how to predict, control and orchestrate self-assembly processes on a precise biomolecular level is essential to the development of new classes of biosensors and bio-mimetic devices.

We model the motor-mediated self-organization of microtubules using a mean-field theory that captures the inherent stochastic nature of motor-filament interactions. Our model reveals that for a sufficiently large motor density, the filament network experiences an ordering transition toward a polar state. In our work we explicitly take into account the specifics of motor dynamics such as force-velocity relations and force-dependent detachment rates. We show that the transition to the oriented state is both continuous and discontinuous when force-dependent motor detachment becomes important. This result predicts an ordering hysteresis for experiments on alignment dynamics in semi-dilute and dense solutions of biological filaments.